variational-backdoor-adjustment

This repository contains the implementation of Variational Backdoor Adjustment (VBA) in the following paper:

Escaping the Curse of High Dimensional Backdoor Adjustment

Authors: Daniel Israel, Guy Van den Broeck, Aditya Grover (link)

Abstract: Backdoor adjustment is an important technique in causal inference for estimating interventional quantities from purely observational data. In medical settings for example, backdoor adjustment can be used to control for confounding and isolate the effectiveness of a treatment. However, high dimensional treatments and confounders pose a series of potential pitfalls. Backdoor adjustment over high dimensional confounders is often intractable. As a remedy, previous approaches often model confounding with latent variables in VAEs, but these methods perform backdoor adjustment over unidentifiable, unobserved variables, leading to inconsistent estimates. In this work, we show that a generative modeling approach can be applied to backdoor adjustment in a fully identified high dimensional setting. Specifically, we cast backdoor adjustment as an optimization problem in variational inference that is constrained by the distribution of a fully observed confounder. Empirically, our method is able to estimate interventional likelihood in a variety of high dimensional settings, including semi-synthetic X-ray medical data. To the best of our knowledge, this is the first application of backdoor adjustment in which all the relevant variables are high dimensional.

Environment Setup

1. Clone the repository.
2. Install the necessary packages with

conda env create -f environment.yml
conda activate variationalbackdoor
pip install -e .

3. To run the code involving autoregressive flow, clone the FFJORD repo and follow the instructions. Please note that these models are more expensive to train than the vanilla neural networks and VAEs used in the experiments.

Usage

A documented example of VBA is given in example.py. Adapting the code for real-world data will likely require a different parameterization of models.

The experiments are divided into linear_gaussian, mnist, and xray.

Linear Gaussian

1. Run train_lg.py
2. For table values, run generate_lg_table.py, then load_lg_table.py
3. For plots, run lg_optimization_plot.py and lg_sampling_plot.py

MNIST

1. Run train_mnist_vae.py and train_mnist_vb.py
2. For plots, run mnist_plot.py

X-Ray

1. Run train_xray.py (Warning: FFJORD must be properly configured and trained separately)
2. For table values, run generate_xray_table.py, then load_xray_table.py
3. For plots, run generate_xray_plot.py, then load_xray_plot.py